Download two physical concepts, ohm and gauss

TWO PHYSICAL CONCEPTS, OHM AND GAUSS
LEILA AZHDARI
Bs.C of Physics, Arsanjan Branch, Islamic Azad University, Arsanjan, Iran
Abstract— Electricity is a fundamental concept applied in industry and factory business. It has some principles raised from
physics science. Electricity has some different branches used in living and industry such as magnetism and electronics.
Electricity physics includes laws and regulations through the science. We investigate two applied laws, Ohm and Gauss in
the paper. These concepts and research presented are got from an annual project.
Keywords— Physics, Electricity, ohm, gauss.
1.
2.
I. OHM’S LAW
Say that you’re wiring a circuit. You know the
amount of current that the component can withstand
without blowing up and how much voltage the power
source applies. So you have to come up with an
amount of resistance that keeps the current below the
blowing-up level.
In the early 1800s, George Ohm published an
equation called Ohm’s Law that allows you to make
this calculation. Ohm’s Law states that the voltage
equals current multiplied by resistance, or in standard
mathematical notation:
V=IxR
The statement of Ohm’s law is simple, and it says
that whenever a potential difference or voltage is
applied across a resistor of a closed circuit, current
starts flowing through it. This current is directly
proportional to the voltage applied if temperature and
all other factors remain constant. Thus we can
mathematically express it as: ∝ Now putting the
constant of proportionality we get, V=I This
particular equation essentially presents the statement
of this law where I is the current through the resistor,
measured in Ampere (Ampere, or amps), when the
electric potential difference V is applied across the
resistor in unit of volt, and ohm(Ω) is the unit of
measure for the resistance of the resistor R. It’s
important to note that the resistance R is the property
of the conductor and theoretically has no dependence
on the voltage applied, or on the flow of current. The
value of R changes only if the conditions (like
temperature, diameter length etc.) of the material are
changed by any means.
3.
There were two copper electrodes X and Y.
Reference electrodes A, B and C are partly
immersed in electrolyte as shown.
A glass container is used to hold the for
electrolyte, as shown.
By observing the results of this experiment, Georg
Simon Ohm had defined the fundamental
interrelationship between current, voltage and
resistance of a circuit which was later named Ohm’s
law . Because of this law and his excellence in the
field of science and academics, he got the Copley
Medal award in 1841. In 1872 the unit of electrical
resistance was named 'OHM" in his honor.
III. GAUSS'S LAW
In physics, Gauss's law, also known as Gauss's flux
theorem, is a law relating the distribution of electric
charge to the resultingelectric field. The law was
formulated by Carl Friedrich Gauss in 1835, but was
not published until 1867. It is one of Maxwell's four
equations, which form the basis of classical
electrodynamics, the other three being Gauss's law
for magnetism, Faraday's law of induction, and
Ampère's law with Maxwell's correction. Gauss's law
can be used to derive Coulomb's law, and vice versa.
It expresses that: The net electric flux through
any closed surface is equal to 1⁄ε times the net electric
charge enclosed within that closed surface.
Gauss's law has a close mathematical similarity with
a number of laws in other areas of physics, such
as Gauss's law for magnetism and Gauss's law for
gravity. In fact, any "inverse-square law" can be
formulated in a way similar to Gauss's law: For
example, Gauss's law itself is essentially equivalent
to the inverse-square Coulomb's law, and Gauss's law
II. HISTORY OF OHM’S LAW
In the month of May 1827, Georg Simon Ohm
published a book by the name ‘Die galvanischeKette,
mathematischbearbeitet’ meaning "The galvanic
circuit investigated mathematically" where he
presented the relationship between voltage(V),
current(I), and resistance(Ω) based on his
experimental data. He performed his experiment with
a simple electro-chemical cell, as shown in the figure
below.
Proceedings of 41st IASTEM International Conference, Paris, France, 15th-16th December 2016, ISBN: 978-93-86291-57-8
14
Two Physical Concepts, Ohm and Gauss on Thermal
for gravity is essentially equivalent to the inversesquare Newton's law of gravity.
Gauss's law is something of an electrical analogue
of Ampère's law, which deals with magnetism.
The law can be expressed mathematically
using vector
calculus
in
integral
form
and differential form, both are equivalent since they
are related by the divergence theorem, also called
Gauss's theorem. Each of these forms in turn can also
be expressed two ways: In terms of a relation
between the electric field E and the total electric
charge, or in terms of the electric displacement
field D and the free electric charge.
 Although Gauss’ Law is a fundamental law of
electrostatics, it mis only of limited use for
finding fields produced by sources
 This is because in integral form it describes an
integration of fields; after a function is
integrated, a lot of information is lost!
 Example: Suppose the electric field flux out of a
surface is zero - is the field on that surface then
necessarily zero?
 It is only possible to use the integral form of
Gauss’ Law for finding fields produced by
particular sources if the sources have a very high
degree of symmetry
 We can also try to find a “differential form” of
Gauss’ Law: one that applies at a point instead of
over some integrated region of space
 To do this, simply shrink the surface S to be
infinitesimally small - leads to the definition of
“divergence”
 We can use the integral form of Gauss’ law to
find the fields produced by a specific set of
charges if the charges possess a high degree of
symmetry
 Based on the symmetry, we can find “Gaussian
surfaces” over which the field has only a normal
component, and on which that component is
constant
 If this is true, the total flux is just the field
component times the surface area; setting this
equal to the charge enclosed determines the
amplitude of the field component
 Types of sources for which this will work: –
infinite line charge (cylindrical coords)
infinite cylinder surface/volume charges
(cylindrical coords) – spherical surface/volume
charges (spherical coords) – surface charges on
an infinite plane (Cartesian coords)
 In all these cases, the line, volume, or surface
charge densities have to be constant
flowing through it. Therefore the resistance R is
viewed as a constant independent of the voltage and
the current.
As these electrons flow through the wire, they are
scattered by atoms in the wire. The resistance of the
circuit is just that; it is a measure of how difficult it is
for the electrons to flow in the presence of such
scattering. This resistance is a property of the circuit
itself, and just about any material has a resistance.
Materials that have a low resistance are called
conductors and materials that have a very high
resistance are called insulators. Some materials have
a moderate resistance and still allow some current to
flow. These are the materials that we use to make
resisters like the ones we will use in this experiment.
In short, the electric potential causes the current to
flow and the resistance impedes that flow.
REFERENCES
CONCLUSIONS
One of the fundamental laws describing how
electrical circuits behave is Ohm’s law. According to
Ohm’s law, there is a linear relationship between the
voltage drop across a circuit element and the current

[1] Serway, Raymond A. (1996). Physics for Scientists and
Engineers with Modern Physics, 4th edition. p. 687.
[2] Grant, W.R. Phillips (2008). Electromagnetism (2nd ed.).
Manchester Physics, John Wiley & Sons. ISBN 978-0-47192712-9.
[3] Grant, W.R. Phillips (2008). Electromagnetism (2nd ed.).
Manchester Physics, John Wiley & Sons. ISBN 978-0-47192712-9.
[4] Matthews, Paul (1998). Vector Calculus. Springer. ISBN 3540-76180-2.
[5] George E. Owen (2003). op. cit.. Mineola, N.Y.: Dover
Publications. p. 285. ISBN 0-486-42830-3.
[6] Billingham, A. C. King (2006). Wave Motion. Cambridge
University Press. p. 179. ISBN 0-521-63450-4.
[7] Slater and N.H. Frank (1969). Electromagnetism (Reprint of
1947 ed.). Courier Dover Publications. p. 83. ISBN 0-48662263-0.
[8] Daniel M. Siegel (2003). Innovation in Maxwell's
Electromagnetic Theory: Molecular Vortices, Displacement
Current, and Light. Cambridge University Press. pp. 96–
98. ISBN 0-521-53329-5.
[9] James C. Maxwell (1861). "On Physical Lines of
Force" (PDF). Philosophical Magazine and Journal of
Science.
[10]Plonsey R. and R.C. Barr. 2007. Bioelectricity: A
Quantitative Approach. 3rd edition,
Springer, New York.
[11]Nicholson, C. and J.A. Freeman. 1975. Theory of current
source-density analysis and determination of conductivity
tensor for
[12]anuran cerebellum J. Neurophysiol. 38: 356-368.
[13]B´edard, C., H. Kr¨oger and A. Destexhe. 2004. Modeling
extracellular field potentials and the frequency-filtering
properties of extracellular space. Biophys. J. 64: 1829-1842.
[14]B´edard, C. and A. Destexhe. 2009. Macroscopic models of
local field potentials and the apparent 1/f noise in brain
activity. Biophys. J. 96: 2589-4608.
[15]Jackson, J.D. 1962. Classical Electrodynamics. John Wiley &
Sons, New York.
[16]Nicholson C. and E. Sykov˜a. 1998. Extracellular space
structure revealed by diffusion analysis Trends Neurosci. 21:
207-215.
[17]B´edard, C., H. Kr¨oger and A. Destexhe. 2006. Model of
low-pass filtering of local field potentials in brain tissue.
Phys. Rev. E 73: 051911.
[18]Bosetti C.A., M.J. Birdno and W.M. Grill. 2008. Analysis of
the quasi-static approximation for calculating potentials
generated by neural stimulation, J Neural Eng ., 5: 25894608.
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